Compliance mismatch is a significant hurdle to long-term patency in small-diameter arterial bypass grafts. Vascular tissue engineering has the potential to produce compliant, non-thrombogenic small-diameter grafts. However, current engineered grafts are relatively non-compliant, resulting in intimal hyperplasia and graft occlusion when subjected to arterial pressures. This research investigates the mechanical and biological properties of engineered constructs based on a biodegradable synthetic elastomer, poly(glycerol sebacate) (PGS). Several methods for fabricating porous PGS scaffolds in a tubular geometry were developed and compared. Adult baboon vascular cells were cultured in the scaffolds under various in vitro experimental conditions, including variations in initial cell seeding density, the type of scaffold used for culture, culture time, scaffold material, and hydrostatic pressure, and properties of the resultant constructs were compared. Scaffold fabrication using heat-shrinkable mandrels and glass tubes coated with hyaluronic acid significantly decreased tolerances of wall thickness and mechanical properties, improved handling, and decreased culture time required to reach luminal cellular confluence compared to scaffolds made with other fabrication techniques. Altering scaffold material from PGS to poly(lactide-co-glycolide) (PLGA), a benchmark biomaterial, did not affect scaffold yield, porosity, or luminal cellular confluence. Extracellular matrix (ECM) deposition increased with SMC-only culture time, and ECM deposition and remodeling during culture influenced construct compliance. Compared to PLGA scaffolds, PGS scaffolds promoted elastin crosslinking by SMCs and elastic tissue properties but attenuated collagen deposition. Hydrostatic pressure promoted ECM synthesis and deposition by SMCs and decreased construct compliance. Collagen and crosslinked elastin content in constructs correlated positively with construct burst pressure, and a negative correlation dependent on scaffold type was found between collagen content and construct compliance at low pressures. The systematic investigation of culture conditions in this research provides insights into the control of engineered blood vessel properties. The central hypothesis of this work, that grafts engineered from PGS scaffolds and adult vascular cells under biomimetic in vitro culture conditions can possess compliance comparable to autologous vessels, is true at pressures below 60 mmHg and demonstrates potential for PGS-based vascular tissue engineering. Overall, this work provides tools for engineering tubular soft tissues based on porous PGS scaffolds.